Table 7 The values of \((q^*_S, q^*_C, q^*_D)\) that maximize the weighted sum throughput \(T_w\) for different values of \(M_U\) when \(\alpha = 0.7\) and the queue at S is unstable
From: A wireless caching helper system with heterogeneous traffic and random availability
\(\delta = 0.5\) | ||||
|---|---|---|---|---|
\(M_U\) | \(w = 1/4\) | \(w = 2/4\) | \(w = 3/4\) | |
200 | max. \(T'_w\) | 0.430 | 0.286 | 0.399 |
\((q^*_S, q^*_C, q^*_D)\) | (0, 1, 0) | (0, 1, 0) | (1, 0.024, 1) | |
400 | max. \(T'_w\) | 0.398 | 0.289 | 0.404 |
\((q^*_S, q^*_C, q^*_D)\) | (0, 1, 0) | (1, 0.029, 1) | (1, 0.005, 1) | |
600 | max. \(T'_w\) | 0.374 | 0.295 | 0.410 |
\((q^*_S, q^*_C, q^*_D)\) | (0, 1, 0) | (1, 0, 1) | (1, 0.011, 1) | |
800 | max. \(T'_w\) | 0.354 | 0.295 | 0.416 |
\((q^*_S, q^*_C, q^*_D)\) | (0, 1, 0) | (1, 0, 1) | (1, 0, 1) | |
1000 | max. \(T'_w\) | 0.337 | 0.298 | 0.422 |
\((q^*_S, q^*_C, q^*_D)\) | (0, 1, 0) | (1, 0, 1) | (1, 0, 1) | |
\(\delta = 1.2\) | ||||
|---|---|---|---|---|
200 | max. \(T'_w\) | 0.189 | 0.363 | 0.537 |
\((q^*_S, q^*_C, q^*_D)\) | (1, 0, 1) | (1, 0, 1) | (1, 0, 1) | |
400 | max. \(T'_w\) | 0.190 | 0.368 | 0.546 |
\((q^*_S, q^*_C, q^*_D)\) | (1, 0.046, 1) | (1, 0, 1) | (1, 0.484, 1) | |
600 | max. \(T'_w\) | 0.190 | 0.371 | 0.552 |
\((q^*_S, q^*_C, q^*_D)\) | (1, 0, 1) | (1, 0, 1) | (1, 0, 1) | |
800 | max. \(T'_w\) | 0.191 | 0.373 | 0.556 |
\((q^*_S, q^*_C, q^*_D)\) | (1, 0, 1) | (1, 0, 1) | (1, 0, 1) | |
1000 | max. \(T'_w\) | 0.191 | 0.375 | 0.559 |
\((q^*_S, q^*_C, q^*_D)\) | (1, 0, 1) | (1, 0, 1) | (1, 0, 1) | |